Significance of few factors among several

[#1]

Hello everyone,

I would like to study an impact of the six factors on evaporation (at the end I would like to have a “rigorous” model with possible interaction effects and power terms):

I already know that the first four have a strong impact on evaporation and would like to know whether the last two (plate load, volume/well) should also be included in the study (model).

How do you suggest to to set up an experiment? Would it be most efficient to first find out whether the two factors (plate load, volume/well) are significant (how to set up a DOE for this purpose?) and then proceed with DOE (augmented DOE?) to get more accurate information about the factors and their (possible) interactions?

Thank you in advance!

Best regards

[#2 · Accepted solution]

Thank you for the explanation.  While I agree with sequential investigation, IMHO, it is better to start with a large design space and hopefully interpolate.  By this I mean lots of factors at bold levels to start.  The issue is inference space.  The smaller the inference space, the less likely the results will hold true in the future (when this conditions invariably change).  If you only experiment on 2 factors, what are the other factors "doing" during this experiment (e.g., are they changing?, are they constant?).  Since you have not quantified nor rank ordered the effect of the 4 factors, why not run a lower resolution 6 factor design with the factors at 2 levels (e.g., 2^6-2 res IV,  16 treatments or 2^6-3 res III, 8 treatments).  The next iterations can help to understand more complex model terms (e.g., non-linear).  At there same time, you might want to run repeats and estimate the factor effects on both the mean and variation of evaporation rate(or at least minimize measurement error).

In the end, I always suggest you design multiple options (no one knows the "best" design á priori.  For each option, predict what you can learn (e.g., what effects can be estimated, which may be confounded and which are not in the study).  Weigh this knowledge against the resource requirements.  Choose one and prepare to iterate.  The purpose of the first experiment is to design a better experiment.

[#3]

I don't understand what do you mean with the "hopefully interpolate".  Could you explain?

[#4]

What is preferred is the design space is large enough to "contain" the optimum conditions (given current materials and technologies).  The you can quickly converge on that optimum.  If your design space is too small, then you will have to move the current space to achieve the optimum (essentially extrapolate).  I will admit, one of the commonest of "errors" in experimental design is to have too narrow of level setting in initial designs.  It seems there is some overt or underlying attempt to find optimum in the first experiment (of course, driven by managements' desire for the one-shot solution).

The reasons we are always searching for optimum and never seem to get there is:

1. We never start our investigations with ALL (we always choose some subset), and

2. New materials and technologies are constantly being invented expanding the dimensional space of investigation